Dimples are used on golf balls to control and improve the flight of the golf ball. The United States Golf Association (U.S.G.A.) requires that golf balls have aerodynamic symmetry. Aerodynamic symmetry allows the ball to fly with little variation no matter how the golf ball is placed on the tee or ground. Preferably, dimples cover the maximum surface area of the golf ball without detrimentally affecting the aerodynamic symmetry of the golf ball.
Most successful dimple patterns are based in general on three of the five existing Platonic Solids: Icosahedron, Dodecahedron or Octahedron. Because the number of symmetric solid body systems is limited, it can be difficult to devise new symmetric patterns.
There are numerous prior art golf balls with different types of dimples or surface textures. The surface textures or dimples of these balls and the patterns in which they are arranged are usually defined by Euclidean geometry.
For example, U.S. Pat. No. 4,960,283 to Gobush discloses a golf ball with multiple types of dimples having dimensions defined by Euclidean geometry. The perimeters of the dimples disclosed in this reference are defined by Euclidean geometric shapes including circles, equilateral triangles, isosceles triangles, and scalene triangles. The surfaces of the dimples are also Euclidean geometric shapes such as partial spheres.
U.S. Pat. No. 5,842,937 to Dalton et al. discloses a golf ball having a surface texture defined by fractal geometry and golf balls having indents whose orientation is defined by fractal geometry. The indents are of varying depths and may be bordered by other indents or smooth portions of the golf ball surface. The surface textures are defined by a variety of fractals including two-dimensional or three-dimensional fractal shapes and objects in complete or partial forms.
As discussed in Mandelbrot's treatise The Fractal Geometry of Nature, many forms in nature are so irregular and fragmented that Euclidean geometry is not adequate to represent them. In his treatise, Mandelbrot identified a family of shapes, which described the irregular and fragmented shapes in nature, and called them fractals. A fractal is defined by its topological dimension DT and its Hausdorf dimension D. DT is always an integer, D need not be an integer, and D is always equal to or greater than DT (See p. 15 of Mandelbrot's The Fractal Geometry of Nature). Fractals may be represented by two-dimensional shapes and three-dimensional objects. In addition, fractals possess self-similarity in that they have the same shapes or structures on both small and large scales. U.S. Pat. No. 5,842,937 uses fractal geometry to define the surface texture of golf balls.
Phyllotaxis is a manner of generating symmetrical patterns or arrangements. Phyllotaxis is defined as the study of the symmetrical pattern and arrangement of leaves, branches, seeds, and petals of plants. See Phyllotaxis A Systemic Study in Plant Morphogenesis by Peter V. Jean, p. 11-12. These symmetric, spiral-shaped patterns are known as phyllotactic patterns. Id. at 11. Several species of plants such as the seeds of sunflowers, pine cones, and raspberries exhibit this type of pattern. Id. at 14-16.
Some phyllotactic patterns have multiple spirals on the surface of an object called parastichies. The spirals have their origin at the center of the surface and travel outward, other spirals originate to fill in the gaps left by the inner spirals. Frequently, the spiral-patterned arrangements can be viewed as radiating outward in both the clockwise and counterclockwise directions. These types of patterns are said to have visibly opposed parastichy pairs denoted by (m, n) where the number of spirals at a distance from the center of the object radiating in the clockwise direction is m and the number of spirals radiating in the counterclockwise direction is n. The angle between two consecutive spirals at their center C is called the divergence angle d. Id. at 16-22.
The Fibonacci-type of integer sequences, where every term is a sum of the previous other two terms, appear in several phyllotactic patterns that occur in nature. The parastichy pairs, both m and n, of a pattern increase in number from the center outward by a Fibonacci-type series. Also, the divergence angle d of the pattern can be calculated from the series. Id.
When modeling a phyllotactic pattern such as with sunflower seeds, consideration for the size, placement and orientation of the seeds must be made. Various theories have been proposed to model a wide variety of plants. These theories can be used to create new dimple patterns for golf balls using the science of phyllotaxis.
There is minimal prior art disclosing the use of the science of phyllotaxis for improving the aerodynamic characteristics for golf balls. U.S. Pat. No. 5,060,953 discloses dimple patterns having dimples extending along intersecting clockwise and counterclockwise arcs extending from each pole to the dimple-free equator. Although phyllotaxis is never cited, the result is something similar. Nevertheless, the disclosed patterns are specifically limited to arcs running from each pole to the equator, establishing a single axis of symmetry. There is no teaching of multiple axes of symmetry with the inherent advantages.
U.S. Pat. Nos. 6,533,684, 6,338,684 and 6,682,441, all owned by the Assignee of the preset invention, are directed to phyllotaxis based dimple patterns that have only two origins (one at each pole) with spirals extending to the equator. Again, this limits them to a single axis of symmetry which is inferior to the multiple axes. These patents, while making an offhand reference to polygonal areas each filled with phyllotactic arrangements of dimples, do not divulge any details.
U.S. Pat. No. 6,699,143 elaborates on the concept of polygonal areas filled with phyllotactic dimple arrangements. However, no specific disclosures or examples are given. Furthermore, it specifically prohibits the overlapping of dimples within the areas, between areas, or over the equator. In contrast, all of the patterns disclosed in the present invention and virtually any pattern developed using its techniques will produce many dimples that overlap the equator. Furthermore, the present invention encourages overlapping dimples both within the areas and between the areas to improve the visual appeal and to enhance performance for lower swing speed golfers.